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We study the N-component (2+1)-dimensional Gross-Neveu model bounded between two parallel planes separated by a distance L at finite temperature (T ). We obtain a closed expression for the large-N effective coupling constant g = g(L, T, λ). Different behavior depending on the magnitude of the fixed coupling constant λ is found to lead to a "critical" value λ c . If λ < λ c , only short-distance and/or high-temperature asymptotic freedom is found. For λ ≥ λ c one also observes spatialdoi:10.1590/s0103-97332007000200019 fatcat:t3mjjrqpwjbaxkskqf2gg2ecni